Calculus Archive: Questions from March 24, 2023
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\( 2 x y y^{\prime}+(x-1) y^{2}=x^{2} e^{x} \quad \operatorname{set}\left(y^{2}=z\right) \) \( y^{\prime}=\sqrt{1-y^{2}} \quad g(0)=\frac{1}{\sqrt{2}} \)2 answers -
3. Evaluate the iterated integral. i) \[ \int_{0}^{1} \int_{x}^{1} \sin \left(y^{2}\right) d y d x \] ii) \[ \int_{0}^{2} \int_{\left(\frac{1}{2}\right) x^{2}}^{2} \sqrt{y} \cos y d y d x \]2 answers -
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1. Solve the given initial value problems: \[ y^{\prime \prime}-4 y^{\prime}+4 y=0, y(0)=12, y^{\prime}(0)=-3 \]2 answers -
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1. (15 puntos) Una planta de fabricación de piezas de polimero cuenta con dos lineas de producción; la linea 1 y la linea 2. En un dia la planta produce 3000 piezas de polimero, de las cuales la lin2 answers -
25 puntos) En un juego de apuestas se requiere extraer dos cartas al azar de una baraja y ue ambas cartas sean ases para poder ganar. (Toma en cuenta que hay 52 cartas de los dales hay 4 ases) Encuent2 answers -
Q.11. Differentiate the functions (a) \( y=\frac{\cos x}{1-\sin x} \) (b) \( y=\sin x^{2}+x \sin \sqrt{x} \).2 answers -
Q.11. Differentiate the functions (a) \( y=\frac{\cos x}{1-\sin x} \), (b) \( y=\sin x^{2}+x \sin \sqrt{x} \).2 answers -
Resuelva \( \frac{d y}{d x}=\frac{y+1}{x} \) \[ \begin{array}{l} \ln |y+1|=c \\ \ln |y+1|=x^{-1}+c \\ \ln |x|+\ln |y+1|=c \\ y=\arctan y+\ln x \\ y=c x-1 \end{array} \]2 answers -
Problem \#4: What is the domain of the function \( f(x, y)=x^{3} y^{1 / 8}-5 \ln x \) ? (A) \( \{(x, y): y>0\} \) (B) \( \{(x, y): x \geq 0, y>0\} \) (C) \( \{(x, y): y \geq 0\} \) (D) \( \{(x, y): x>2 answers -
6. Prove that if a vectorfield \( \mathbf{F}(x, y, z)=(M(x, y, z), N(x, y, z), P(x, y, z)) \) in space is conservative, then \[ \frac{\partial f}{\partial y}(x, y, z)=N(x, y, z) \] for some differenti2 answers -
Q.11. Differentiate the functions (a) \( y=\frac{\cos x}{1-\sin x} \) (b) \( y=\sin x^{2}+x \sin \sqrt{x} \).2 answers -
Q.6. Find (a) \( \lim _{x \rightarrow 2} \frac{x^{3}-2 x^{2}+4 x-8}{x^{4}-2 x^{3}+x-2} \), (b) \( \lim _{x \rightarrow 0} \frac{\sin 8 x}{x} \).2 answers -
1. Find \( f^{\prime}(x) \) if \( f(x)=\frac{x^{2}+1}{e^{x}} \). [A] \( \frac{1-x^{2}}{e^{x}} \) [B] \( \frac{(x+1)^{2}}{e^{x}} \) [C] \( -\frac{(x+1)^{2}}{e^{x}} \) [D] \( -\frac{(x-1)^{2}}{e^{x}} \)2 answers -
2. Find \( f^{\prime}(0) \) if \( f(x)=\tan x \sec x \). [A] 0 [B] 1 [C] \( \frac{1}{2} \) [D] 2 [E] \( \frac{1}{4} \)2 answers -
Please help ASAP
Find the gradient \( \nabla f(x, y) \) of the function \( f(x y)=\sin (x y) \). \[ \begin{array}{r} y \cos (x y)+x \cos (x y) \\ \langle y \sin (x y), x \sin (x y)\rangle \\ \langle x \sin (x y), y \s2 answers -
only the second part b and c , please. II. Determine and interpret the curvature K of the curve at the given parameter value.
I. Determine la longitud del arco en el intervalo dado a) \( r(t)=i+t^{2} j+t^{3} k ;[0,2] \) b) \( r(t)=\langle 4 t,-\cos t, \operatorname{sen} t\rangle ;\left[0, \frac{3 \pi}{2}\right] \) II. Determ2 answers -
4: What is the domain of the function \( f(x, y)=x^{4} y^{1 / 7}-9 \ln x \) ? (A) \( \{(x, y): y \geq 0\} \quad \) (f \( \quad\{(x, y): x>0\} \) (C) \( \{(x, y): y>0\} \) (D) \( \{(x, y): x \geq 0, y2 answers -
\( \iint_{\mathcal{R}} \frac{x y}{1+x^{4}} d A, \quad \mathcal{R}:=\{(x, y):-1 \leq x \leq 1,0 \leq y \leq 1\} \)2 answers -
Please Help!
If \( y=\Phi(x) \) is a solution to the differential equation \[ \begin{array}{ll} & y^{\prime \prime}+(\sin x) y^{\prime}+(\cos x) y=0 ; y(0)=4 y^{\prime}(0)=1 \\ \Phi^{\prime \prime}(0)= & , \\ \Phi2 answers -
Consider the region \( R \) in the first quadrant that is bounded by \( y=2-x^{2}, y=0 \), and \( y=x \). If for any function \( f(x, y) \) we have \( \iint_{R} f(x, y) d A=\int_{0}^{1} \int_{g_{1}(y)2 answers -
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Find the first partial derivatives of the furiction. \[ \begin{array}{l} f(x, y, z)=3 x \sin (y-z) \\ f_{x}(x, y, z)= \\ f_{y}(x, y, z)= \\ f_{z}(x, y, z)= \end{array} \]2 answers -
I would like to know about how this problem goes.
3. Obtén los puntos crÃticos para la función \( z=f(x, y) \), aplica el criterio de las segundas derivadas parciales a cada punto crÃtico obtenido para determinar si existe ahà un máximo, un mÃ2 answers -
Use logarithmic differentiation to find \( y^{\prime} \). \[ y=\frac{\sqrt{3-8 x}\left(x^{2}+7\right)^{2}}{x^{2}+7 x+7} \] \[ y^{\prime}= \]2 answers -
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Compute the curl, \( \nabla \times \mathbf{F} \), of the vector fields in Exercises 13 to 16 . 13. \( \mathbf{F}(x, y, z)=x \mathbf{i}+y \mathbf{j}+z \mathbf{k} \) 15. \( \mathbf{F}(x, y, z)=\left(x^{2 answers -
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Compute the curl, \( \nabla \times \mathbf{F} \), of the vector fields in Exercises 13 to 16 . 13. \( \mathbf{F}(x, y, z)=x \mathbf{i}+y \mathbf{j}+z \mathbf{k} \) 15. \( \mathbf{F}(x, y, z)=\left(x^{2 answers -
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1. Realice una pregunta para verificar 0 ampliar una información. 2. Comparta su comentario inicial y compárelo con el de su compañero. 3. Ofrezca sugerencias sobre el comentario. 4. Valide ideas c2 answers -
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En esta actividad usted contestará los ejercicios de práctica que se presentan a continuación. Es necesario que muestre su procedimiento claro y completo para que obtenga crédito parcial o total.2 answers -
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Find the partial derivatives of the function \[ f(x, y)=x y e^{7 y} \] \[ \begin{array}{l} f_{x}(x, y)=e^{7 y_{y}} \\ f_{y}(x, y)=x e^{7 y}(7 y+1) \\ f_{x y}(x, y)= \\ f_{y x}(x, y)= \end{array} \]2 answers -
Problem 1 Evaluate the double integral. \[ \iint_{D} e^{-y^{2}} d A, \quad D=\{(x, y) \mid 0 \leqslant y \leqslant 3,0 \leqslant x \leqslant y\} \]2 answers -
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Evaluate the following surface integrals \( \iint_{S}(\nabla \times \mathbf{F}) \cdot d \mathbf{S} \). 1. \( \mathbf{F}(x, y, z)=y \mathbf{i}-x \mathbf{j}+z x^{3} y^{2} \mathbf{k} \) and \( S=\left\{(2 answers -
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PLEASE SOLVE
2. Let \( g(x, y)=\sqrt{x} / y \). Use a tangent plane or differentials to approximate \( g(4.01,-2.02) \).2 answers -
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